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2017 AMC 10A Problem 13

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2017 AMC 10A Problem 13AMC 10 Step by Step

Name: Date: September 13, 2026

Modular Arithmetic · difficulty 2 of 5 · about 3 min · position P11-15

Define a sequence recursively by $F_{0}=0,~F_{1}=1,$ and $F_{n}=$ the remainder when $F_{n-1}+F_{n-2}$ is divided by $3,$ for all $n\geq 2.$ Thus the sequence starts $0,1,1,2,0,2,\ldots$ What is $F_{2017}+F_{2018}+F_{2019}+F_{2020}+F_{2021}+F_{2022}+F_{2023}+F_{2024}?$

A)
$6$
B)
$7$
C)
$8$
D)
$9$
E)
$10$

2017 AMC 10A Problem 13

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